Q: I have a new iPhone 5S.  My children are receiving my calls and can see my texts on their phone and iPads,

Settings>Facetime>Cellular Calls = off

You can turn off the calls by going to Settings > FaceTime and change "iPhone Cellular Calls" to off on each device.

It is a feature of Continuity: Use Continuity to connect your iPhone, iPad, iPod touch, and Mac - Apple Support which also has information re the text messages.

You should consider using separate Apple IDs for each family member. This is now more flexible with Family Sharing: https://www.apple.com/icloud/family-sharing/

Even better, stop sharing an ID for iCloud, Messages, and FaceTime.

Stop sharing an Apple ID.

Despite setting up separate icloud account for each of my daughters, they are still seeing my messages. I want them to be able to message me and their grandparents so don't want to turn it off, Is there another setting I can adjust?

Ctrots wrote:

 

Despite setting up separate icloud account for each of my daughters, they are still seeing my messages. I want them to be able to message me and their grandparents so don't want to turn it off, Is there another setting I can adjust?

Then you didn't do it correctly. You need to wipe their devices (follow the instructions here: What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support) and then set them back up from scratch using their IDs.

Ctrots wrote:

 

Despite setting up separate icloud account for each of my daughters, they are still seeing my messages. I want them to be able to message me and their grandparents so don't want to turn it off, Is there another setting I can adjust?

It sounds as if maybe you didn't log out of iMessage on their devices. Log out then log back in using the new Apple IDs you created for them.

Thanks heaps.

Hope it helped!